The couple have been separated since July, according to the singer's rep.
Marx's separation from Rhodes was first revealed on Katie on Friday, when Katie Couric asked the singer what it's like to be "back on the market."
"It's all brand new to me, so I'm just having fun," Marx said.
The "Right Here Waiting" singer and Dirty Dancing actress met in 1983 on the set of Staying Alive. The couple married in 1989 and have three kids together, Brandon, 23, Lucas, 21, and Jesse, 20.